OrthodoxMan

2 years ago

A 5000-kg truck drives over a pothole in the road that causes thetruck to push down on all four springs a distance of 4.0 cm. If energy is conserved and the springs obey Hooke’s law, calculate thespring constant for each sprin

Force caused by gravity is:
F = m(-g) = -mg = -(5000kg)(9.8N/kg) (negative means downward)
F = -49000 N (negative means downward)
F = k(Δy)
-49000 = k(-4) (Δy is negative because the initial position is at 0 meters and the final position is at -4 metres so Δy = -4 - 0 = -4 metres. Also notice that Δy being negative means that the truck went downward by 4 meters when the pot hole was hit.)
(When people say F = -kx, you treat x as the distance that was moved while ignoring the sign but the way I did it makes you systematically think about it.)
-49000/(-4) = 49000/4 = k = 12250 N/m (This is the spring constant - it means that in order to move the spring by 1 meter from its natural position where it would remain if nothing was forcefully compressing or stretching it, 12250 N of force would be required.)